Mathematics
In the given figure, ABCD is a parallelogram and X, Y are points on diagonal BD such that DX = BY. Prove that CXAY is a parallelogram.
Related Questions
In the adjoining figure, ABCD is a parallelogram and X is the mid-point of BC. The line AX produced meets DC produced at Q. The parallelogram AQPB is completed. Prove that :
(i) ΔABX ≅ ΔQCX.
(ii) DC = CQ = QP.
In the adjoining figure, ABCD is a parallelogram. Line segments AX and CY bisect ∠A and ∠C respectively. Prove that :
(i) ΔADX ≅ ΔCBY
(ii) AX = CY
(iii) AX ∥ CY
(iv) AYCX is a parallelogram
Show that the bisectors of the angles of a parallelogram enclose a rectangle.
If a diagonal of a parallelogram bisects one of the angles of the parallelogram, prove that it also bisects the second angle and then the two diagonals are perpendicular to each other.